Topology of tropical moduli spaces of weighted stable curves in higher genus
Abstract
Given integers $g \geq 0$, $n \geq 1$, and a vector $w \in (\mathbb{Q} \cap (0, 1])^n$ such that ${2g  2 + \sum w_i > 0}$, we study the topology of the moduli space $\Delta_{g, w}$ of $w$stable tropical curves of genus $g$ with volume 1. The space $\Delta_{g, w}$ is the dual complex of the divisor of singular curves in Hassett's moduli space of $w$stable genus $g$ curves $\overline{\mathcal{M}}_{g, w}$. When $g \geq 1$, we show that $\Delta_{g, w}$ is simply connected for all values of $w$. We also give a formula for the Euler characteristic of $\Delta_{g, w}$ in terms of the combinatorics of $w$.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.11767
 arXiv:
 arXiv:2010.11767
 Bibcode:
 2020arXiv201011767K
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Geometry;
 14T05
 EPrint:
 14 pages